Part of my sphere disappears when in BGE
Only switch of backface culling when you need to see both sides of the face at the same time and both sides should have the same material (it doubles the faces!). Use cases: glass, leaves, paper, curtain

In your case you ALWAYS want to see the inner side of the half-dome. This means you model is incorrect as you can see the outside only. To change that go into edit mode and flip the normals w.